Subgroups — #25002138

Order 11008.

1186 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583665	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582915	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582901	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582670	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582667	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134315	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	#14583665	—	2	2	no	—
10	#14583665	—	2	2	no	—
11	#14583665	—	2	2	no	—
12	#14583665	C₄	1	4	yes	complemented
13	C₂×#13063333	—	2	2	no	—
14	C₂×#13063331	—	2	2	no	—
15	C₂²×#10621877	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×D₄₃	—	2	2	no	—
17	C₂×#13063284	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
19	#14582915	—	2	2	no	—
20	#14582915	C₄	1	4	yes	complemented
21	C₂×#13063251	—	2	2	no	—
22	#14582901	—	2	2	no	—
23	#14582901	—	2	2	no	—
24	C₂×#13063250	C₄	1	2	yes	complemented
25	C₂×#13063247	C₄	1	2	yes	complemented
26	#14582670	—	2	2	no	—
27	#14582667	—	2	2	no	—
28	#14582662	—	2	2	no	—
29	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#338	—	2	2	no	—
33	C₂×#10621898	—	2	1	no	—
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	C₂×C₄	1	2	yes	—
40	C₂×#10621898	C₂×C₄	1	2	yes	—
41	C₂×#10621898	D₄	1	2	yes	—
42	C₂×#10621898	D₄	1	2	yes	—
43	C₂×#10621898	D₄	1	2	yes	—
44	C₂×#10621898	Q₈	1	2	yes	—
45	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₃	—	2	1	no	—
48	C₂³×Dic₄₃	—	2	1	no	—
49	C₂²×C₄×D₄₃	—	2	1	no	—
50	#13063333	—	2	8	no	—
51	#13063333	—	2	8	no	—
52	#13063331	—	2	8	no	—
53	#13063331	—	2	8	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂×#10621877	—	2	1	no	—
57	C₂×#10621877	C₂×C₄	1	2	yes	—
58	C₂×#10621877	D₄	1	2	yes	—
59	C₂×#10621877	D₄	1	2	yes	—
60	C₂×#10621872	—	2	4	no	—
61	M₁₆×D₄₃	—	2	8	no	—
62	M₁₆×D₄₃	—	2	8	no	—
63	C₂²×C₄₃⋊C₈	—	2	1	no	—
64	C₂×C₈×D₄₃	—	2	4	no	—
65	#13063284	—	2	1	no	—
66	#13063284	—	2	1	no	—
67	#13063284	—	2	1	no	—
68	#13063284	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊Dic₄₃	—	2	1	no	—
70	C₂×C₄⋊Dic₄₃	—	2	1	no	—
71	C₂×C₄⋊Dic₄₃	—	2	1	no	—
72	C₂×C₄⋊Dic₄₃	—	2	1	no	—
73	C₂×C₄⋊Dic₄₃	—	2	1	no	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
77	C₂×C₄×Dic₄₃	—	2	1	no	—
78	#13063251	—	2	8	no	—
79	#13063250	—	2	4	no	—
80	#13063247	—	2	4	no	—
81	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₄₃	—	2	1	no	—
83	C₂×M₁₆×C₄₃	—	2	1	no	—
84	C₂×M₁₆×C₄₃	—	2	1	no	—
85	C₂×M₁₆×C₄₃	—	2	1	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	—	2	1	no	—
93	C₂×M₁₆×C₄₃	—	2	1	no	—
94	C₂×M₁₆×C₄₃	—	2	1	no	—
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂×M₁₆×C₄₃	—	2	1	no	—
97	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
98	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
99	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
100	C₂²×C₈×C₄₃	—	2	1	no	—
101	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
102	C₂²×C₈×C₄₃	D₄	1	2	yes	—
103	C₂⁴×C₄₃	#41	1	1	yes	characteristic
104	C₂³×D₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₃	—	2	2	no	—
120	C₂×C₂²⋊D₄₃	—	2	2	no	—
121	C₂×C₂²⋊D₄₃	—	2	2	no	—
122	C₂×C₂²⋊D₄₃	—	2	2	no	—
123	C₂×C₂²⋊D₄₃	—	2	2	no	—
124	C₂×C₂²⋊D₄₃	—	2	2	no	—
125	C₂²×Dic₄₃	—	2	1	no	—
126	C₂²×Dic₄₃	—	2	2	no	—
127	C₂²×Dic₄₃	—	4	1	no	—
128	C₂²×Dic₄₃	—	4	1	no	—
129	C₂²×Dic₄₃	—	4	1	no	—
130	C₂²×Dic₄₃	—	8	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	2	2	no	—
140	#10621898	—	2	2	no	—
141	#10621898	—	2	2	no	—
142	#10621898	—	2	2	no	—
143	#10621898	C₂²⋊C₄	1	4	yes	—
144	#10621898	C₂²⋊C₄	1	4	yes	—
145	#10621898	C₄⋊C₄	1	4	yes	—
146	#10621898	C₄⋊C₄	1	4	yes	—
147	C₂×D₁₇₂	—	2	1	no	—
148	C₂×D₁₇₂	—	2	1	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	C₄²	1	2	yes	—
151	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
152	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
153	C₂×C₄×D₄₃	—	2	2	no	—
154	C₂×C₄×D₄₃	—	2	2	no	—
155	C₂×C₄×D₄₃	—	2	2	no	—
156	C₂×C₄×D₄₃	—	2	2	no	—
157	C₂×C₄×D₄₃	—	2	2	no	—
158	C₂×C₄×D₄₃	—	2	2	no	—
159	C₂×Dic₈₆	—	2	1	no	—
160	C₂×Dic₈₆	—	2	1	no	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	C₄²	1	2	yes	—
163	C₂×Dic₈₆	C₂²⋊C₄	1	2	yes	—
164	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
165	M₁₆×C₄₃	—	2	2	no	—
166	M₁₆×C₄₃	—	2	2	no	—
167	M₁₆×C₄₃	—	2	2	no	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	—	2	2	no	—
170	M₁₆×C₄₃	—	2	2	no	—
171	M₁₆×C₄₃	—	4	1	no	—
172	M₁₆×C₄₃	—	4	1	no	—
173	M₁₆×C₄₃	—	4	1	no	—
174	M₁₆×C₄₃	—	4	1	no	—
175	M₁₆×C₄₃	—	4	1	no	—
176	M₁₆×C₄₃	—	4	1	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	—	2	2	no	—
179	C₂×C₈×C₄₃	—	2	2	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	—	2	2	no	—
182	C₂×C₈×C₄₃	—	2	2	no	—
183	C₂×C₈×C₄₃	—	4	1	no	—
184	C₂×C₈×C₄₃	—	4	1	no	—
185	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
186	C₂²⋊Dic₄₃	—	2	2	no	—
187	C₂²⋊Dic₄₃	—	4	1	no	—
188	C₄⋊Dic₄₃	—	2	2	no	—
189	C₄⋊Dic₄₃	—	2	2	no	—
190	C₄⋊Dic₄₃	—	2	2	no	—
191	C₄⋊Dic₄₃	—	4	1	no	—
192	C₄⋊Dic₄₃	—	4	1	no	—
193	C₄⋊Dic₄₃	—	4	1	no	—
194	C₄×Dic₄₃	—	2	2	no	—
195	C₄×Dic₄₃	—	4	1	no	—
196	#10621877	—	2	2	no	—
197	#10621877	—	2	2	no	—
198	#10621877	—	2	2	no	—
199	#10621877	C₂²⋊C₄	1	4	yes	—
200	C₂×C₄₃⋊C₈	—	2	2	no	—
201	C₂×C₄₃⋊C₈	—	2	2	no	—
202	C₂×C₄₃⋊C₈	—	2	2	no	—
203	#10621872	—	2	16	no	—
204	C₈×D₄₃	—	2	16	no	—
205	C₂³×C₄₃	—	4	1	no	—
206	C₂³×C₄₃	—	4	1	no	—
207	C₂³×C₄₃	#117	1	1	yes	characteristic
208	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₄₃	#121	1	1	yes	characteristic
211	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂³×C₄₃	#123	1	1	yes	characteristic
213	C₂³×C₄₃	#123	1	1	yes	characteristic
214	C₂²×D₄₃	—	2	2	no	—
215	C₂²×D₄₃	—	2	2	no	—
216	C₂²×D₄₃	—	2	2	no	—
217	C₂²×D₄₃	—	8	1	no	—
218	C₂²×D₄₃	—	8	1	no	—
219	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
239	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
246	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
247	C₂²⋊D₄₃	—	2	4	no	—
248	C₂²⋊D₄₃	—	2	4	no	—
249	C₂²⋊D₄₃	—	2	4	no	—
250	C₂²⋊D₄₃	—	2	4	no	—
251	C₂×Dic₄₃	—	2	2	no	—
252	C₂×Dic₄₃	—	2	2	no	—
253	C₂×Dic₄₃	—	2	2	no	—
254	C₂×Dic₄₃	—	4	2	no	—
255	C₂×Dic₄₃	—	4	2	no	—
256	C₂×Dic₄₃	—	8	1	no	—
257	C₂×Dic₄₃	—	8	1	no	—
258	C₂×Dic₄₃	—	8	2	no	—
259	C₂×Dic₄₃	—	8	2	no	—
260	C₂×Dic₄₃	—	8	2	no	—
261	D₁₇₂	—	2	2	no	—
262	D₁₇₂	—	2	2	no	—
263	D₁₇₂	—	2	2	no	—
264	D₁₇₂	#95	1	4	yes	—
265	C₄×D₄₃	—	2	4	no	—
266	C₄×D₄₃	—	2	4	no	—
267	C₄×D₄₃	—	2	4	no	—
268	C₄×D₄₃	—	2	4	no	—
269	Dic₈₆	—	2	2	no	—
270	Dic₈₆	—	2	2	no	—
271	Dic₈₆	—	2	2	no	—
272	Dic₈₆	#95	1	4	yes	—
273	C₈×C₄₃	—	2	4	no	—
274	C₈×C₄₃	—	4	2	no	—
275	C₈×C₄₃	—	4	2	no	—
276	C₄₃⋊C₈	—	2	4	no	—
277	#10784	—	43	1	no	maximal, Sylow
278	C₂²×C₄₃	—	2	1	no	—
279	C₂²×C₄₃	—	2	1	no	—
280	C₂²×C₄₃	—	2	1	no	—
281	C₂²×C₄₃	—	2	1	no	—
282	C₂²×C₄₃	—	2	1	no	—
283	C₂²×C₄₃	—	2	1	no	—
284	C₂²×C₄₃	—	4	1	no	—
285	C₂²×C₄₃	—	4	1	no	—
286	C₂²×C₄₃	—	4	1	no	—
287	C₂²×C₄₃	—	4	1	no	—
288	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₄₃	#380	1	1	yes	characteristic
290	C₂²×C₄₃	#381	1	1	yes	characteristic
291	C₂²×C₄₃	#385	1	1	yes	characteristic
292	C₂²×C₄₃	#385	1	1	yes	characteristic
293	C₂²×C₄₃	#386	1	1	yes	characteristic
294	C₂²×C₄₃	#386	1	1	yes	characteristic
295	C₂×D₄₃	—	2	4	no	—
296	C₂×D₄₃	—	4	2	no	—
297	C₂×D₄₃	—	4	2	no	—
298	C₂×D₄₃	—	8	2	no	—
299	C₂×D₄₃	—	8	2	no	—
300	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
301	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
302	C₄×C₄₃	#379	1	1	yes	characteristic
303	C₄×C₄₃	#380	1	1	yes	characteristic
304	C₄×C₄₃	#385	1	1	yes	characteristic
305	C₄×C₄₃	#385	1	1	yes	characteristic
306	C₄×C₄₃	#386	1	1	yes	characteristic
307	C₄×C₄₃	#386	1	1	yes	characteristic
308	Dic₄₃	—	2	4	no	—
309	Dic₄₃	—	8	2	no	—
310	Dic₄₃	—	8	2	no	—
311	C₂×#568	—	43	1	no	—
312	C₂×#421	—	43	1	no	—
313	C₂×#417	—	43	1	no	—
314	C₂×#344	—	43	1	no	—
315	C₂×#343	—	43	1	no	—
316	#1736	—	43	1	no	—
317	C₂×#338	D₄₃	1	1	yes	characteristic, complemented
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	—	2	1	no	—
324	C₂×C₄₃	C₂²⋊#95	1	1	yes	characteristic
325	C₂×C₄₃	#1902	1	1	yes	characteristic
326	C₂×C₄₃	#1903	1	1	yes	characteristic
327	D₄₃	—	4	4	no	—
328	C₂²×#41	—	43	1	no	—
329	#568	—	43	4	no	—
330	#568	—	86	2	no	—
331	#568	—	86	2	no	—
332	#568	—	86	2	no	—
333	C₂×#131	—	86	2	no	—
334	C₂×#131	—	86	2	no	—
335	C₂²×M₁₆	—	43	1	no	—
336	C₂²×M₁₆	—	86	2	no	—
337	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
338	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
339	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
340	C₂×#117	—	43	1	no	—
341	C₂²×C₄⋊C₄	—	43	1	no	—
342	#421	—	43	4	no	—
343	#421	—	86	2	no	—
344	C₂×#104	—	86	2	no	—
345	#417	—	86	2	no	—
346	#417	—	86	2	no	—
347	C₂×#103	—	43	2	no	—
348	C₂×#102	—	43	2	no	—
349	#344	—	86	2	no	—
350	#343	—	86	2	no	—
351	#340	—	86	2	no	—
352	#338	—	2	2	no	—
353	C₄₃	#10784	1	1	yes	characteristic, complemented, Sylow
354	C₂×#41	—	43	2	no	—
355	C₂×#41	—	43	2	no	—
356	C₂×#41	—	43	2	no	—
357	C₂×#41	—	43	2	no	—
358	C₂×#41	—	43	2	no	—
359	C₂×#41	—	43	2	no	—
360	C₂×#41	—	86	1	no	—
361	C₂×#41	—	86	1	no	—
362	C₂×#41	—	86	1	no	—
363	C₂×#41	—	86	1	no	—
364	C₂×#41	—	86	1	no	—
365	C₂×#41	—	86	1	no	—
366	C₂²×Q₈	—	43	1	no	—
367	C₂²×D₄	—	43	1	no	—
368	C₂²×D₄	—	86	1	no	—
369	C₂³×C₄	—	86	1	no	—
370	C₂³×C₄	—	86	1	no	—
371	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
372	#131	—	86	8	no	—
373	#131	—	86	8	no	—
374	#131	—	86	8	no	—
375	#131	—	86	8	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	43	2	no	—
392	C₂×M₁₆	—	43	2	no	—
393	C₂×M₁₆	—	43	2	no	—
394	C₂×M₁₆	—	86	4	no	—
395	C₂×M₁₆	—	86	8	no	—
396	C₂×M₁₆	—	86	8	no	—
397	C₂×M₁₆	—	86	1	no	—
398	C₂×M₁₆	—	86	1	no	—
399	C₂×M₁₆	—	86	1	no	—
400	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
401	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
402	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	86	4	no	—
405	C₂²×C₈	—	86	1	no	—
406	C₂²×C₈	C₄×D₄₃	1	2	yes	—
407	C₂²×C₈	D₁₇₂	1	2	yes	—
408	#117	—	43	2	no	—
409	#117	—	86	1	no	—
410	#117	—	86	1	no	—
411	#117	—	86	1	no	—
412	C₂×C₄⋊C₄	—	43	2	no	—
413	C₂×C₄⋊C₄	—	86	1	no	—
414	C₂×C₄⋊C₄	—	86	1	no	—
415	C₂×C₄⋊C₄	—	86	1	no	—
416	C₂×C₄⋊C₄	—	86	1	no	—
417	C₂×C₄⋊C₄	—	86	1	no	—
418	C₂×C₄⋊C₄	—	86	1	no	—
419	C₂×C₂²⋊C₄	—	86	1	no	—
420	C₂×C₄²	—	86	1	no	—
421	#104	—	86	8	no	—
422	#103	—	86	4	no	—
423	#102	—	86	4	no	—
424	C₂⁴	—	86	1	no	—
425	C₂⁴	#10621902	1	1	yes	characteristic
426	#41	—	43	4	no	—
427	#41	—	43	4	no	—
428	#41	—	43	4	no	—
429	#41	—	43	4	no	—
430	#41	—	86	2	no	—
431	#41	—	86	2	no	—
432	#41	—	86	2	no	—
433	#41	—	86	2	no	—
434	#41	—	86	2	no	—
435	#41	—	86	2	no	—
436	#41	—	86	2	no	—
437	#41	—	86	2	no	—
438	#41	—	86	2	no	—
439	#41	—	86	2	no	—
440	#41	—	86	2	no	—
441	#41	—	86	2	no	—
442	C₂×Q₈	—	43	2	no	—
443	C₂×Q₈	—	43	2	no	—
444	C₂×Q₈	—	43	2	no	—
445	C₂×Q₈	—	86	1	no	—
446	C₂×Q₈	—	86	1	no	—
447	C₂×Q₈	—	86	1	no	—
448	C₂×D₄	—	43	2	no	—
449	C₂×D₄	—	43	2	no	—
450	C₂×D₄	—	43	2	no	—
451	C₂×D₄	—	86	2	no	—
452	C₂×D₄	—	86	2	no	—
453	C₂×D₄	—	86	2	no	—
454	C₂×D₄	—	86	2	no	—
455	C₂×D₄	—	86	2	no	—
456	C₂×D₄	—	86	2	no	—
457	C₂×D₄	—	86	1	no	—
458	C₂×D₄	—	86	1	no	—
459	C₂×D₄	—	86	1	no	—
460	C₂²×C₄	—	86	1	no	—
461	C₂²×C₄	—	86	2	no	—
462	C₂²×C₄	—	86	2	no	—
463	C₂²×C₄	—	86	2	no	—
464	C₂²×C₄	—	86	2	no	—
465	C₂²×C₄	—	86	2	no	—
466	C₂²×C₄	—	86	2	no	—
467	C₂²×C₄	—	86	2	no	—
468	C₂²×C₄	—	344	2	no	—
469	C₂²×C₄	—	172	1	no	—
470	C₂²×C₄	—	172	1	no	—
471	C₂²×C₄	—	172	1	no	—
472	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
476	C₂²×C₄	#10621898	1	1	yes	characteristic
477	C₂²×C₄	#10621898	1	1	yes	characteristic
478	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
479	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
480	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
481	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
482	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
483	C₂²×C₄	#10621900	1	1	yes	characteristic
484	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	2	2	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	4	1	no	—
493	M₁₆	—	4	1	no	—
494	M₁₆	—	4	1	no	—
495	M₁₆	—	4	1	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	43	4	no	—
499	M₁₆	—	86	16	no	—
500	M₁₆	—	86	2	no	—
501	M₁₆	—	86	2	no	—
502	M₁₆	—	86	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	4	1	no	—
510	C₂×C₈	—	4	1	no	—
511	C₂×C₈	—	86	16	no	—
512	C₂×C₈	—	86	2	no	—
513	C₂×C₈	—	86	2	no	—
514	C₂×C₈	—	86	2	no	—
515	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
516	C₄⋊C₄	—	86	2	no	—
517	C₄⋊C₄	—	86	2	no	—
518	C₄⋊C₄	—	86	2	no	—
519	C₄⋊C₄	—	172	1	no	—
520	C₄⋊C₄	—	172	1	no	—
521	C₄⋊C₄	—	172	1	no	—
522	C₂²⋊C₄	—	86	2	no	—
523	C₂²⋊C₄	—	172	1	no	—
524	C₄²	—	86	2	no	—
525	C₄²	—	172	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	86	2	no	—
529	C₂³	—	86	2	no	—
530	C₂³	—	86	2	no	—
531	C₂³	—	344	1	no	—
532	C₂³	—	344	1	no	—
533	C₂³	#13063283	1	1	yes	characteristic
534	C₂³	#13063287	1	1	yes	characteristic
535	C₂³	#13063287	1	1	yes	characteristic
536	C₂³	#13063300	1	1	yes	characteristic
537	C₂³	#13063301	1	1	yes	characteristic
538	C₂³	#13063310	1	1	yes	characteristic
539	C₂³	#13063310	1	1	yes	characteristic
540	Q₈	—	43	4	no	—
541	Q₈	—	86	2	no	—
542	Q₈	—	86	2	no	—
543	Q₈	—	86	2	no	—
544	D₄	—	43	4	no	—
545	D₄	—	86	4	no	—
546	D₄	—	86	4	no	—
547	D₄	—	86	4	no	—
548	D₄	—	86	4	no	—
549	D₄	—	86	2	no	—
550	D₄	—	86	2	no	—
551	D₄	—	86	2	no	—
552	C₂×C₄	—	86	2	no	—
553	C₂×C₄	—	86	2	no	—
554	C₂×C₄	—	86	2	no	—
555	C₂×C₄	—	86	4	no	—
556	C₂×C₄	—	86	4	no	—
557	C₂×C₄	—	86	4	no	—
558	C₂×C₄	—	86	4	no	—
559	C₂×C₄	—	344	2	no	—
560	C₂×C₄	—	344	2	no	—
561	C₂×C₄	—	344	1	no	—
562	C₂×C₄	—	344	1	no	—
563	C₂×C₄	—	344	2	no	—
564	C₂×C₄	—	172	2	no	—
565	C₂×C₄	—	172	2	no	—
566	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
567	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
568	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
569	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
570	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
571	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
573	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
574	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
575	C₂×C₄	#13063282	1	1	yes	characteristic
576	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
577	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
578	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
579	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
580	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
581	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
582	C₂×C₄	#13063293	1	1	yes	characteristic
583	C₂×C₄	#13063293	1	1	yes	characteristic
584	C₂×C₄	#13063295	1	1	yes	characteristic
585	C₂×C₄	#13063295	1	1	yes	characteristic
586	C₂×C₄	#13063296	1	1	yes	characteristic
587	C₂×C₄	#13063298	1	1	yes	characteristic
588	C₂×C₄	#13063298	1	1	yes	characteristic
589	C₂×C₄	#13063303	1	1	yes	characteristic
590	C₂×C₄	#13063303	1	1	yes	characteristic
591	C₂×C₄	#13063305	1	1	yes	characteristic
592	C₂×C₄	#13063307	1	1	yes	characteristic
593	C₂×C₄	#13063307	1	1	yes	characteristic
594	C₈	—	2	4	no	—
595	C₈	—	4	2	no	—
596	C₈	—	4	2	no	—
597	C₈	—	86	4	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	86	4	no	—
609	C₂²	—	344	2	no	—
610	C₂²	—	344	2	no	—
611	C₂²	—	172	2	no	—
612	C₂²	—	172	2	no	—
613	C₂²	#14582746	1	1	yes	characteristic
614	C₂²	#14582756	1	1	yes	characteristic
615	C₂²	#14582761	1	1	yes	characteristic
616	C₂²	#14582770	1	1	yes	characteristic
617	C₂²	#14582770	1	1	yes	characteristic
618	C₂²	#14582777	1	1	yes	characteristic
619	C₂²	#14582777	1	1	yes	characteristic
620	C₄	—	86	4	no	—
621	C₄	—	344	2	no	—
622	C₄	—	344	2	no	—
623	C₄	#95×D₄₃	1	1	yes	characteristic
624	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
625	C₄	#14582754	1	1	yes	characteristic
626	C₄	#14582758	1	1	yes	characteristic
627	C₄	#14582773	1	1	yes	characteristic
628	C₄	#14582773	1	1	yes	characteristic
629	C₄	#14582775	1	1	yes	characteristic
630	C₄	#14582775	1	1	yes	characteristic
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	172	4	no	—
638	C₂	(C₂×D₄₃)⋊#95	1	1	yes	characteristic
639	C₂	#19135069	1	1	yes	characteristic
640	C₂	#19135076	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14582777
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#338	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#338	D₄₃
hypocenter	C₄₃	#10784
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#338

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂×#14582670	C₂	semidirect
5. C₂×#14582667	C₂	semidirect
6. #19134315	C₂	semidirect
7. C₂×C₄₃×#338	C₂	semidirect
12. #14583665	C₄	semidirect
20. #14582915	C₄	semidirect
24. C₂×#13063250	C₄	semidirect
25. C₂×#13063247	C₄	semidirect
317. C₂×#338	D₄₃	semidirect
353. C₄₃	#10784	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14583665	2
C₂×#14582915	2
C₂×#14582901	2
C₂×#14582670	2
C₂×#14582667	2
#19134315	2
C₂×C₄₃×#338	2
#10784	43